Numerical and analytical studies of physical properties of 2D antiferromagnetic spin systems

Fu-Jiun Jiang

The numerical value of a universal quantity associated with the quantum critical regime, namely χuc2/T, for a two-dimensional (2D) dimerized spin-1/2 antiferromagnet is calculated using the quantum Monte Carlo simulations (QMC). Here χu, c, and T are the uniform susceptibility, the spin-wave velocity, and the temperature, respectively. By simulating large lattices at moderately low temperatures, we find χuc2/T∼0.32. Our estimation of χuc2/T deviates from the related analytic prediction but agrees with recent numerical calculations of other 2D dimerized spin-1/2 antiferromagnets.

Eric S. Swanson

Makoto Yajima

H. Q. Lin, David K Campbell

Applying a renormalization-group (RG) procedure to the 2D antiferromagnetic Heisenberg (AFH) model, we derive an effective AFH model in which spins on a 1D ring experience antiferromagnetic nearest-neighbor interactions and iteract individually with an effective central spin. Using analytic and numerical arguments, we establish the existence of staggered long-range order in the effective model and hence, given our RG prescription, in the 2D AFH. Our RG calculations give a value of the magnetic moment consistent with Monte Carlo results for the 2D AFH.

Makoto Kaburagi, Takashi Tonegawa, T. Nishino

Gang Chen, Ming Gong, Chuanwei Zhang

The recent experimental realization of spin-orbit coupling for ultracold atoms has generated much interest in the physics of spin-orbit-coupled degenerate Fermi gases. Although recently the BCS-BEC crossover in three-dimensional (3D) spin-orbit-coupled Fermi gases has been intensively studied, the corresponding two-dimensional (2D) crossover physics has remained unexplored. In this paper, we investigate, both numerically and analytically, the BCS-BEC crossover physics in 2D degenerate Fermi gases in the presence of the Rashba type of spin-orbit coupling. We derive the mean-field gap and atom-number equations suitable for 2D spin-orbit-coupled Fermi gases and solve them numerically and self-consistently, from which the dependence of the ground-state properties (chemical potential, superfluid pairing gap, ground-state energy per atom) on the system parameters (e.g., binding energy, spin-orbit-coupling strength) is obtained. Furthermore, we derive analytical expressions for these ground-state quantities, which agree well with our numerical results within a broad parameter region. Such analytical expressions also agree qualitatively with previous numerical results for 3D spin-orbit-coupled Fermi gases, where analytical results are lacking. We show that, with increasing spin-orbit coupling (SOC) strength, the chemical potential is shifted by a constant determined by the SOC strength. The superfluid pairing gap is enhanced significantly in the BCS limit for strong SOC, but increases only slightly in the BEC limit.